Convergence of age-sex distributions and population change in the presence of migration

Abstract

In recent years considerable interest has been shown for analytical research in demography. With the increased application of matrix methods, it is becoming possible to investigate problems more thoroughly than before. In the earlier studies, the effects of fertility and mortality on the growth and age-sex composition of human populations were examined extensively both through theoretical and empirical investigations. But it appeared that the effects of introducing migration into the process of population change had not received the same attention. When migration was included, two procedures had been used: one in which a set of age-sex-specific net migration rates was assumed, and another in which an overall net migration rate and an age-sex composition of net migrants (i.e. of net number of migrants) were assumed. In almost all theoretical investigations the first procedure had been followed. This reduced the mathematical difficulties because the age-sex-specific net migration rates, suitably defined, could be incorporated into the survival rates. But the procedure is not suited to examine the effects of either a given overall net migration rate or of a specified age-sex composition of net migrants on the growth and the changes in the age-sex distribution of a population. These can be studied only when the second procedure is adopted. Hence, an attempt is made in this study to examine, analytically, the effects of migration on the growth and the changes in the age-sex structure of a population when migration is specified by an overall net migration rate and an age-sex composition of net migrants at the time of migration. The results in the absence of migration are used as the standard of reference to compare the effects of migration. The investigations are carried through the use of deterministic models of one sex and two sexes. The one-sex case is used only for analytical convenience, and the results are always extended to the two-sex case. "The outcomes of numerical illustrations using the two-sex model are presented. The effects of migration when it is specified by age-sex-specific net migration rates, are also given for comparison. After presenting, in Chapter 2, the results of an analysis of the numerical data used in the illustrations, the problem of the convergence of age-sex distributions is taken up for investigation. In Chapter 3, the following questions are studied: Whether, as in the case of a closed population, an unchanging age-sex distribution and a constant growth rate are evolved if a constant set of fertility, mortality and migration schedules operates on an arbitrary age-sex distribution over a long period of time?, and How would the time required for this convergence (the duration of convergence) be changed due to the inclusion of migration into the population process? Then Chapter 4 deals with a natural generalization and examines the convergence of two arbitrary age-sex distributions when they are subjected to identical schedules of fertility, mortality and migration that are varying over time. The changes in the duration of convergence due to the presence of migration are studied in this case also. Next, the relationship between the growth and the changes in the age-sex structure of a population on the one hand, and the operating schedules of fertility, mortality and migration on the other, is examined both when the operating conditions remain constant over time and vary over time. Under the assumption of constant schedules, two situations are considered: one in which a set of single schedule of each of the components operates constantly over time, and another in which a set of k schedules of each operates repeatedly over time. In the first case, a constant growth rate (i.e., the intrinsic growth rate) and a constant age-sex distribution (i.e., the equilibrium state age-sex distribution) are evolved, while in the second a stable set of k growth rates and k age-sex distributions is evolved. Hence, Chapter 5 concentrates on the derivation of expressions which show explicitly the relationship between these characteristics of the ultimate populations and the given schedules of fertility, mortality and migration. On the other hand, when the operating schedules are changing over time, no fixed growth rate or age-sex distribution is obtained. But both are changed over time due to the operation of the components of change. Hence, in the final chapter, an attempt is made to assess the contribution of the changes in the components during a certain period of time towards the changes in the characteristics of the population during that period. A method called the factorial projections method, is suggested for this purpose and is applied to study the changes in the population of Australia during 1911-66. Show more